Definition:Exponential Family of Distributions
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Definition
Let $P$ be a probability distribution.
$P$ is a member of the exponential family of distributions if and only if it has a probability density function of the form:
- $\map f {x, h} = \map \exp {\map a x \map b h + \map c h + \map d x}$
where $h$ is a parameter whose value is to be determined.
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Also see
- Results about the exponential family of distributions can be found here.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): exponential family of distributions
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): exponential family of distributions